统计/概率学术速递[7.25]

math.ST统计，共计13篇

math.PR概率，共计11篇

1.math.ST统计:

【1】LSD of sample covariances of superposition of matrices with separable covariance structure
标题 ：具有可分离协方差结构的矩阵叠加的样本协方差的LSD
链接 ：https://arxiv.org/abs/2507.18505

作者 ：arika, Debashis Paul
摘要 ：We study the asymptotic behavior of the spectra of matrices of the form $S_n = \frac{1}{n}XX^*$ where $X =\sum_{r=1}^K X_r$, where $X_r = A_r^\frac{1}{2}Z_rB_r^\frac{1}{2}$, $K \in \mathbb{N}$ and $A_r,B_r$ are sequences of positive semi-definite matrices of dimensions $p\times p$ and $n\times n$, respectively. We establish the existence of a limiting spectral distribution for $S_n$ by assuming that matrices $\{A_r\}_{r=1}^K$ are simultaneously diagonalizable and $\{B_r\}_{r=1}^K$ are simultaneously digaonalizable, and that the joint spectral distributions of $\{A_r\}_{r=1}^K$ and $\{B_r\}_{r=1}^K$ converge to $K$-dimensional distributions, as $p,n\to \infty$ such that $p/n \to c \in (0,\infty)$. The LSD of $S_n$ is characterized by system of equations with unique solutions within the class of Stieltjes transforms of measures on $\mathbb{R}_+$. These results generalize existing results on the LSD of sample covariances when the data matrices have a separable covariance structure.
摘要

【2】ROC curves for LDA classifiers
标题 ：LDA分类器的ROC曲线
链接 ：https://arxiv.org/abs/2507.18307

作者 ：rukowski
摘要 ：在本文中，我们推导出LDA分类器的ROC曲线的解析公式。我们建立了这些曲线的基本性质（单调性和非单调性），并提供了曲线下面积（AUC）和Youden J指数的公式。
摘要 ：In the paper, we derive an analytic formula for the ROC curves of the LDA classifiers. We establish elementary properties of these curves (monotonicity and concavity) and provide formulae for the area under curve (AUC) and the Youden J-index.

【3】Data assimilation with the 2D Navier-Stokes equations: Optimal Gaussian asymptotics for the posterior measure
标题 ：用2D Navier-Stokes方程进行数据同化：后验测量的最佳高斯渐进性
链接 ：https://arxiv.org/abs/2507.18279

作者 ：nen, Richard Nickl
摘要 ：本文对二维Navier-Stokes方程的数据同化问题证明了一个泛函Bernstein-vonMises定理，其中高斯过程先验被赋予系统的初始条件。的后验测量，它提供了在空间中的所有轨迹所产生的（确定性）动态的离散样本的更新，被证明是近似的高斯随机向量场所产生的解决方案，以高斯初始条件的线性抛物型偏微分方程。近似持有强意义上的上确界规范的回归函数，表明预测未来状态的Navier-Stokes系统承认1/\sqrt N$-一致的估计，即使是常用的非参数模型。覆盖的可信波段和不确定性量化的后果进行了讨论。一个局部渐近极大极小定理，推导出描述的下界估计的非线性系统，这是达到贝叶斯数据同化算法的状态。
摘要 ：A functional Bernstein - von Mises theorem is proved for posterior measures arising in a data assimilation problem with the two-dimensional Navier-Stokes equation where a Gaussian process prior is assigned to the initial condition of the system. The posterior measure, which provides the update in the space of all trajectories arising from a discrete sample of the (deterministic) dynamics, is shown to be approximated by a Gaussian random vector field arising from the solution to a linear parabolic PDE with Gaussian initial condition. The approximation holds in the strong sense of the supremum norm on the regression functions, showing that predicting future states of Navier-Stokes systems admits $1/\sqrt N$-consistent estimators even for commonly used nonparametric models. Consequences for coverage of credible bands and uncertainty quantification are discussed. A local asymptotic minimax theorem is derived that describes the lower bound for estimating the state of the nonlinear system, which is shown to be attained by the Bayesian data assimilation algorithm.

【4】Trek-Based Parameter Identification for Linear Causal Models With Arbitrarily Structured Latent Variables
标题 ：具有临时结构潜在变量的线性因果模型的基于Trek的参数识别
链接 ：https://arxiv.org/abs/2507.18170

作者 ：ma, Mathias Drton
摘要 ：我们发展了一个准则，以证明是否因果效应是可识别的线性结构方程模型的潜在变量。线性结构方程模型对应于有向图，其节点表示感兴趣的随机变量，其边用对应于直接因果效应的线性系数加权。与先前的识别方法相比，我们不将自己限制于潜变量构成独立潜因子的设置（即，到模型的图形表示中的源节点）。我们的新的潜在子图标准是一个纯粹的图形条件，这是足够的因果关系的协方差矩阵中的合理公式的可识别性。为了检查潜在子图准则，我们提供了一个健全的和完整的算法，通过求解一个整数线性规划。虽然它的目标是涉及观测变量的影响，但我们的新标准对于识别潜在变量之间的影响也很有用，因为它允许将给定模型转换为其他现有工具适用的更简单的测量模型。
摘要 ：We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables of interest and whose edges are weighted with linear coefficients that correspond to direct causal effects. In contrast to previous identification methods, we do not restrict ourselves to settings where the latent variables constitute independent latent factors (i.e., to source nodes in the graphical representation of the model). Our novel latent-subgraph criterion is a purely graphical condition that is sufficient for identifiability of causal effects by rational formulas in the covariance matrix. To check the latent-subgraph criterion, we provide a sound and complete algorithm that operates by solving an integer linear program. While it targets effects involving observed variables, our new criterion is also useful for identifying effects between latent variables, as it allows one to transform the given model into a simpler measurement model for which other existing tools become applicable.

【5】Bounding Conditional Value-at-Risk via Auxiliary Distributions with Bounded Discrepancies
标题 ：通过具有有界差异的辅助分布确定有界条件风险价值
链接 ：https://arxiv.org/abs/2507.18129

作者 ：riente, Vadim Indelman
摘要 ：在本文中，我们开发了一个理论框架，使用另一个相关的随机变量$Y $的随机变量$X$的CVaR的边界，假设其累积和密度函数。我们的结果产生了实用的工具，近似$\operatorname{CVaR}_\alpha（X）$时，直接信息$X$是有限的，或采样是计算昂贵的，通过利用一个更易处理或可观察的随机变量$Y$。此外，推导出的界限提供了可解释的浓度不等式，量化了如何通过Y控制X的尾部风险。
摘要 ：In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for approximating $\operatorname{CVaR}_\alpha(X)$ when direct information about $X$ is limited or sampling is computationally expensive, by exploiting a more tractable or observable random variable $Y$. Moreover, the derived bounds provide interpretable concentration inequalities that quantify how the tail risk of $X$ can be controlled via $Y$.

【6】Zeroth-order log-concave sampling
标题 ：零阶log-凹抽样
链接 ：https://arxiv.org/abs/2507.18021

作者 ：ok
备注 ：30 pages
摘要 ：We study the zeroth-order query complexity of log-concave sampling, specifically uniform sampling from convex bodies using membership oracles. We propose a simple variant of the proximal sampler that achieves the query complexity with matched R\'enyi orders between the initial warmness and output guarantee. Specifically, for any $\varepsilon>0$ and $q\geq2$, the sampler, initialized at $\pi_{0}$, outputs a sample whose law is $\varepsilon$-close in $q$-R\'enyi divergence to $\pi$, the uniform distribution over a convex body in $\mathbb{R}^{d}$, using $\widetilde{O}(qM_{q}^{q/(q-1)}d^{2}\,\lVert\operatorname{cov}\pi\rVert\log\frac{1}{\varepsilon})$ membership queries, where $M_{q}=\lVert\text{d}\pi_{0}/\text{d}\pi\rVert_{L^{q}(\pi)}$. We further introduce a simple annealing scheme that produces a warm start in $q$-R\'enyi divergence (i.e., $M_{q}=O(1)$) using $\widetilde{O}(qd^{2}R^{3/2}\,\lVert\operatorname{cov}\pi\rVert^{1/4})$ queries, where $R^{2}=\mathbb{E}_{\pi}[|\cdot|^{2}]$. This interpolates between known complexities for warm-start generation in total variation and R\'enyi-infinity divergence. To relay a R\'enyi warmness across the annealing scheme, we establish hypercontractivity under simultaneous heat flow and translate it into an improved mixing guarantee for the proximal sampler under a logarithmic Sobolev inequality. These results extend naturally to general log-concave distributions accessible via evaluation oracles, incurring additional quadratic queries.
摘要

【7】An omnibus goodness-of-fit test based on trigonometric moments
标题 ：基于三角矩的综合适合度检验
链接 ：https://arxiv.org/abs/2507.18591

作者 ：gagné, Frédéric Ouimet
备注 ：65 pages, 6 figures, 36 tables
摘要 ：我们提出了一个通用的综合拟合优度检验的基础上的前两个三角矩的概率积分转换的数据，纠正了协方差缩放误差的Langholz和Kronmal [J. Amer.统计。Assoc.86（1991），1077- 1084]。一旦正确缩放，二次型统计量在零假设下渐近遵循$\chi_2^2$分布。协方差标度和参数估计提供了32 $零分布的家庭，包括重尾，轻尾，不对称和有界支持的情况下，所以测试是准备直接应用。利用最新进展的非退化多元U$-统计估计滋扰参数，我们还展示了其渐近分布下的本地替代品的三个具体例子。我们的程序显示出出色的力量，特别是，模拟测试拉普拉斯模型对一系列的400美元的替代品显示，它超过了所有40美元现有的测试中，大样本量。一个包含48小时前地表温度预报误差的实际数据应用进一步证明了该测试的实用性。为了确保完全的可重复性，生成我们数值结果的R代码可在线公开访问。
摘要 ：We present a versatile omnibus goodness-of-fit test based on the first two trigonometric moments of probability-integral-transformed data, which rectifies the covariance scaling errors made by Langholz and Kronmal [J. Amer. Statist. Assoc. 86 (1991), 1077--1084]. Once properly scaled, the quadratic-form statistic asymptotically follows a $\chi_2^2$ distribution under the null hypothesis. The covariance scalings and parameter estimators are provided for $32$ null distribution families, covering heavy-tailed, light-tailed, asymmetric, and bounded-support cases, so the test is ready to be applied directly. Using recent advances in non-degenerate multivariate $U$-statistics with estimated nuisance parameters, we also showcase its asymptotic distribution under local alternatives for three specific examples. Our procedure shows excellent power; in particular, simulations testing the Laplace model against a range of $400$ alternatives reveal that it surpasses all $40$ existing tests for moderate to large sample sizes. A real-data application involving 48-hour-ahead surface temperature forecast errors further demonstrates the practical utility of the test. To ensure full reproducibility, the R code that generated our numerical results is publicly accessible online.

【8】How weak are weak factors? Uniform inference for signal strength in signal plus noise models
标题 ：弱势因素有多弱？信号加噪音模型中信号强度的统一推断
链接 ：https://arxiv.org/abs/2507.18554

作者 ：ovskaya, Vadim Gorin, Sasha Sodin
备注 ：75 pages, 6 figures
摘要 ：本文分析了四种经典的信号加噪声模型：因子模型、加标样本协方差矩阵、Wigner矩阵与低秩扰动之和以及具有低秩依赖的典型相关分析。目标是为信号强度构建置信区间，该置信区间在所有状态（强、弱和关键信号）中均有效。我们表明，传统的高斯近似失败的关键制度。相反，我们引入了一个通用的过渡分布，使有效的推断在整个频谱的信号强度。该方法通过在宏观经济学和金融中的应用加以说明。
摘要 ：The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The objective is to construct confidence intervals for the signal strength that are uniformly valid across all regimes - strong, weak, and critical signals. We demonstrate that traditional Gaussian approximations fail in the critical regime. Instead, we introduce a universal transitional distribution that enables valid inference across the entire spectrum of signal strengths. The approach is illustrated through applications in macroeconomics and finance.

【9】Euclidean Distance Deflation Under High-Dimensional Heteroskedastic Noise
标题 ：多维异方差噪音下的欧几里得距离缩窄
链接 ：https://arxiv.org/abs/2507.18520

作者 ：Yuval Kluger, Boris Landa
摘要 ：成对欧氏距离计算是许多机器学习和数据分析算法中的基本步骤。然而，在现实世界的应用中，这些距离经常被异方差噪声扭曲，这是一种普遍存在的非均匀腐败形式，其特征在于数据观测中的可变噪声幅度。这种噪声以一种非平凡的方式膨胀了计算的距离，导致底层数据几何的错误表示。在这项工作中，我们解决的任务，估计每个观察的噪声幅度和校正下的异方差噪声的成对欧几里德距离。也许令人惊讶的是，我们表明，在一般的高维设置，并没有假设先验知识的干净的数据结构或噪声分布，这两个任务可以可靠地执行，即使当噪声水平变化很大。具体来说，我们开发了一种原则性的，无超参数的方法，联合估计噪声幅度和校正的距离。我们为我们的方法提供理论保证，建立噪声幅度和距离的估计误差的概率界。这些界限，在规范化的$\ell_1$范数测量，收敛到零的多项式率的特征维数和数据集大小的增加。在合成数据集上的实验表明，我们的方法在具有挑战性的制度中准确地估计距离，显着提高了后续基于距离的计算的鲁棒性。值得注意的是，当应用于单细胞RNA测序数据时，我们的方法产生与已建立的原型模型一致的噪声幅度估计，从而实现准确的最近邻识别，这对于许多下游分析至关重要。
摘要 ：Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a prevalent form of inhomogeneous corruption characterized by variable noise magnitudes across data observations. Such noise inflates the computed distances in a nontrivial way, leading to misrepresentations of the underlying data geometry. In this work, we address the tasks of estimating the noise magnitudes per observation and correcting the pairwise Euclidean distances under heteroskedastic noise. Perhaps surprisingly, we show that in general high-dimensional settings and without assuming prior knowledge on the clean data structure or noise distribution, both tasks can be performed reliably, even when the noise levels vary considerably. Specifically, we develop a principled, hyperparameter-free approach that jointly estimates the noise magnitudes and corrects the distances. We provide theoretical guarantees for our approach, establishing probabilistic bounds on the estimation errors of both noise magnitudes and distances. These bounds, measured in the normalized $\ell_1$ norm, converge to zero at polynomial rates as both feature dimension and dataset size increase. Experiments on synthetic datasets demonstrate that our method accurately estimates distances in challenging regimes, significantly improving the robustness of subsequent distance-based computations. Notably, when applied to single-cell RNA sequencing data, our method yields noise magnitude estimates consistent with an established prototypical model, enabling accurate nearest neighbor identification that is fundamental to many downstream analyses.

【10】On Reconstructing Training Data From Bayesian Posteriors and Trained Models
标题 ：关于从Bayesian后验和训练模型重建训练数据
链接 ：https://arxiv.org/abs/2507.18372

作者 ：nne
摘要 ：公开发布模型的规范及其训练参数意味着对手可以尝试通过训练数据重建攻击来重建有关训练数据的信息，这是现代机器学习方法的一个主要漏洞。本文主要有三个贡献：建立一个数学框架来表达这个问题，通过最大平均差异等价性来描述训练数据的特征，并概述了贝叶斯和非贝叶斯模型中重建数据的得分匹配框架，前者是文献中的第一个。
摘要 ：Publicly releasing the specification of a model with its trained parameters means an adversary can attempt to reconstruct information about the training data via training data reconstruction attacks, a major vulnerability of modern machine learning methods. This paper makes three primary contributions: establishing a mathematical framework to express the problem, characterising the features of the training data that are vulnerable via a maximum mean discrepancy equivalance and outlining a score matching framework for reconstructing data in both Bayesian and non-Bayesian models, the former is a first in the literature.

【11】Moment Martingale Posteriors for Semiparametric Predictive Bayes
标题 ：半参数预测Bayes的矩Martingale后验
链接 ：https://arxiv.org/abs/2507.18148

作者 ：ung, Stephen M.S. Lee, Edwin Fong
备注 ：19 pages (main), 45 pages (total), 15 figures, 3 tables
摘要 ：预测贝叶斯视图涉及引出一系列一步预测分布，而不是指定似然函数和先验分布。最近的方法已经利用了预测分布，这些预测分布是非参数的或参数的，但不是两者的组合。本文介绍了一种半参数鞅后验，它利用的预测分布，是一个参数和非参数成分的混合。半参数性质的预测允许正则化的非参数组件时，样本量很小，和鲁棒性的参数组件时，样本量很大的模型误指定。我们把这种方法称为矩鞅后验，因为我们提出的方法的核心是利用矩的方法作为车辆绑在一起的非参数和参数组件。特别是，预测构造，使时刻是鞅，这使我们能够验证下的预测reserve收敛。这项工作的一个关键贡献是一个新的程序的基础上的能量分数，以最佳的参数和非参数组件之间的权重，它具有理想的渐近性质。通过仿真和一个真实世界的例子证明了所提出的方法的有效性。
摘要 ：The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are either nonparametric or parametric, but not a combination of the two. This paper introduces a semiparametric martingale posterior which utilizes a predictive distribution that is a mixture of a parametric and nonparametric component. The semiparametric nature of the predictive allows for regularization of the nonparametric component when the sample size is small, and robustness to model misspecification of the parametric component when the sample size is large. We call this approach the moment martingale posterior, as the core of our proposed methodology is to utilize the method of moments as the vehicle for tying the nonparametric and parametric components together. In particular, the predictives are constructed so that the moments are martingales, which allows us to verify convergence under predictive resampling. A key contribution of this work is a novel procedure based on the energy score to optimally weigh between the parametric and nonparametric components, which has desirable asymptotic properties. The effectiveness of the proposed approach is demonstrated through simulations and a real world example.

【12】Large-scale entity resolution via microclustering Ewens--Pitman random partitions
标题 ：基于微聚类Ewens-Pitman随机划分的大规模实体分辨
链接 ：https://arxiv.org/abs/2507.18101

作者 ：aha, Stefano Favaro
摘要 ：我们介绍了微聚类Ewens-Pitman模型的随机分区，通过缩放的Ewens-Pitman模型的强度参数与样本大小线性。由此产生的随机分区示出具有微聚类属性，即：最大的集群的大小与样本大小呈次线性增长，而集群的数量呈线性增长。通过利用Ewens-Pitman随机划分与Pitman-Yor过程之间的相互作用，我们开发了有效的变分推理方案，用于实体分辨率的后验计算。我们的方法实现了三个数量级的速度比现有的贝叶斯方法的实体分辨率，同时保持竞争力的经验性能。
摘要 ：We introduce the microclustering Ewens--Pitman model for random partitions, obtained by scaling the strength parameter of the Ewens--Pitman model linearly with the sample size. The resulting random partition is shown to have the microclustering property, namely: the size of the largest cluster grows sub-linearly with the sample size, while the number of clusters grows linearly. By leveraging the interplay between the Ewens--Pitman random partition with the Pitman--Yor process, we develop efficient variational inference schemes for posterior computation in entity resolution. Our approach achieves a speed-up of three orders of magnitude over existing Bayesian methods for entity resolution, while maintaining competitive empirical performance.

【13】Sliding Window Informative Canonical Correlation Analysis
标题 ：滑动窗口信息典型相关分析
链接 ：https://arxiv.org/abs/2507.17921

作者 ：asadan
备注 ：22 pages, submitted
摘要 ：典型相关分析（CCA）是一种用于发现两个数据集之间相关特征集的技术。在本文中，我们提出了一种新的扩展CCA的在线，流数据设置：滑动窗口信息典型相关分析（SWICCA）。我们的方法使用流主成分分析（PCA）算法作为后端，并使用这些输出结合一个小的滑动窗口的样本来估计CCA组件的实时。我们激励和描述我们的算法，提供数值模拟来表征其性能，并提供理论性能保证。SWICCA方法是适用的，可扩展到极高的维度，我们提供了一个真实的数据的例子，证明了这一能力。
摘要 ：Canonical correlation analysis (CCA) is a technique for finding correlated sets of features between two datasets. In this paper, we propose a novel extension of CCA to the online, streaming data setting: Sliding Window Informative Canonical Correlation Analysis (SWICCA). Our method uses a streaming principal component analysis (PCA) algorithm as a backend and uses these outputs combined with a small sliding window of samples to estimate the CCA components in real time. We motivate and describe our algorithm, provide numerical simulations to characterize its performance, and provide a theoretical performance guarantee. The SWICCA method is applicable and scalable to extremely high dimensions, and we provide a real-data example that demonstrates this capability.

2.math.PR概率:

【1】Global fluctuations for standard Young tableaux
标题 ：标准年轻场景的全球波动
链接 ：https://arxiv.org/abs/2507.18601

作者 ：aposo
备注 ：82 pages
摘要 ：我们介绍的概念，一个年轻的生成函数的概率测度整数分区。我们用这个对象来刻画概率分布整数分区满足大数定律和那些满足中心极限定理。我们进一步建立了一个多级中心极限定理，这使得研究随机标准Young tableaux成为可能。作为这些结果的应用，我们描述了与（i）Plancherel增长过程，（ii）固定形状的随机标准Young tableaux，和（iii）由无限对称群$S\infty$的极端特征引起的概率分布相关的高度函数的涨落。在所有情况下，我们确定的限制波动作为一个条件高斯自由场。
摘要 ：We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that satisfy a central limit theorem. We further establish a multilevel central limit theorem, which enables the study of random standard Young tableaux. As applications of these results, we describe the fluctuations of height functions associated with (i) the Plancherel growth process, (ii) random standard Young tableaux of fixed shape, and (iii) probability distributions induced by extreme characters of the infinite symmetric group $S_\infty$. In all cases, we identify the limiting fluctuations as a conditioned Gaussian Free Field.

【2】Consistency of tug-of-war type operators on random data clouds
标题 ：随机数据云上拉锯式操作符的一致性
链接 ：https://arxiv.org/abs/2507.18383

作者 ：Han, Huajie Liu
摘要 ：本文研究了几何图上的一个拔河型算子及其在随机数据云上的Dirichlet问题。 具体来说，我们分析的收敛值函数的数据点的数量增加和游戏的步长缩小。这一分析揭示了我们的拔河型算子和相应的模型问题之间的联系。 确定这一结果的一个关键因素是操作者的一致性。
摘要 ：In this paper, we study a tug-of-war type operator on geometric graphs and its associated Dirichlet problem on a random data cloud. Specifically, we analyze the convergence of the value functions as the number of data points increases and the step size of the game shrinks. This analysis reveals the connection between our tug-of-war type operator and the corresponding model problem. A key ingredient in establishing this result is the consistency of the operator.

【4】An upper bound of the lower tail of the mass of balls under the critical $2d$ stochastic heat flow
标题 ：临界$2d$随机热流下球质量下尾的上界
链接 ：https://arxiv.org/abs/2507.18080

作者 ：kashima
摘要 ：我们研究临界二维随机热流$\mathscr{Z}_t^{\vartheta}$，最近构造的有向聚合物在随机环境中的标度极限和作为一个软化的随机热方程的解的极限.针对球$\mathscr{Z}_t^{\vartheta}（B_r（0），B_r（a））$（$a\in \mathbb{R}^2$，$r>0$）的质量，建立了其下尾的一个上界.作为结果，我们证明了$\mathscr{Z}_t^{\vartheta}（B_r（0），B_r（a））$的对数的可积性及其严格正性.这些结果提供了部分答案，开放的问题有关的本地行为的$\mathscr{Z}_t^\vartheta$。
摘要 ：We study the critical two-dimensional stochastic heat flow $\mathscr{Z}_t^{\vartheta}$, recently constructed as the scaling limit of directed polymers in a random environment and as the limit of the solution to a mollified stochastic heat equation. Focusing on the mass of balls $\mathscr{Z}_t^{\vartheta}(B_r(0),B_r(a))$ ($a\in \mathbb{R}^2$, $r>0$), we establish an upper bound on its lower tail. As a consequence, we prove the integrability of the logarithm of $\mathscr{Z}_t^{\vartheta}(B_r(0),B_r(a))$ and its strict positivity. These results provide partial answers to open questions concerning the local behavior of $\mathscr{Z}_t^\vartheta$.

【5】Spectral analysis of $q$-deformed unitary ensembles with the Al-Salam--Carlitz weight
标题 ：具有Al-Salam--Carlitz权的$q$-变形么正系综的谱分析
链接 ：https://arxiv.org/abs/2507.18042

作者 ：Byun, Yeong-Gwang Jung, Jaeseong Oh
备注 ：25 pages, 6 figures
摘要 ：我们研究了q变形随机酉系综与权函数的Al-Salam-Carlitz正交多项式，索引的参数$a 0$是固定的，我们得到的前两项在大-$N$展开的谱矩。因此，我们得到了封闭形式的极限谱密度的表达式。值得注意的是，这个密度表现出两个连续的相变作为$\lambda$增加，其特征在于减少软边缘的数量从两个，到一个，并最终到没有。此外，我们表明，极限密度符合极限零分布的Al-Salam-Carlitz正交多项式在相同的标度。
摘要 ：We study $q$-deformed random unitary ensembles associated with the weight function of the Al-Salam--Carlitz orthogonal polynomials, indexed by a parameter $a 0$ is fixed, we derive the first two terms in the large-$N$ expansion of the spectral moments. As a consequence, we obtain a closed-form expression for the limiting spectral density. Notably, this density exhibits two successive phase transitions as $\lambda$ increases, characterised by a reduction in the number of soft edges from two, to one, and eventually to none. Furthermore, we show that the limiting density coincides with the limiting zero distribution of the Al-Salam--Carlitz orthogonal polynomials under the same scaling.

【7】Periodic TASEP and a Cylindrical dual-RSK
标题 ：定期TASDP和圆柱形双RSK
链接 ：https://arxiv.org/abs/2507.17954

作者 ：ar
摘要 ：我们介绍一个版本的RSK，捕捉定期TASEP的动态。这项工作是建立一个圆柱形的类似物（AB Dieker，J Warren，2008年）。
摘要 ：We introduce a version of RSK that captures the dynamics of periodic TASEP. This work is building towards a cylindrical analogue of (AB Dieker, J Warren, 2008).

【8】Critical non-local spatial branching processes with infinite variance conditioned on survival
标题 ：以生存为条件的具有无限方差的关键非局部空间分支过程
链接 ：https://arxiv.org/abs/2507.17858

作者 ：ardona-Tobón, Andreas E. Kyprianou, Pedro Martín-Chávez
备注 ：1 figure
摘要 ：我们考虑一般的非局部分支粒子过程或一般的非局部超过程的设置。假设平均半群有一个Perron Frobenious型行为结合一个经常变化的假设，允许无限的再生点过程，我们考虑充分条件，确保有限的分配稳定性条件下生存在临界状态。 我们提供两个主要结果。在上述条件下，我们的第一个主要贡献建立多项式衰减的时间的生存概率的精神，经典的柯尔莫哥洛夫极限。第二个主要贡献涉及稳定性，当生存条件下，在一个Yaglom限制的精神。在这两种情况下，我们的证明同样适用于具有非局部分支的非局部超过程的类似设置。 我们的结果完善了20世纪50年代至70年代各种非空间分支过程族的一系列文章，并补充了Ren最近关于空间分支过程的这类结果，Song和Sun（2020）我们的结果的一般性改进了Hering和Hoppe（1981）和Asmussen和Hering（1983）的旧工作他处理了分支粒子系统的类似背景，并为非局部超过程提供了一个通用框架。
摘要 ：We consider the setting of either a general non-local branching particle process or a general non-local superprocess. Under the assumption that the mean semigroup has a Perron-Frobenious type behaviour in combination with a regularly varying assumption on the reproductive point process, which permits infinite second moments, we consider sufficient conditions that ensure limiting distributional stability when conditioned on survival at criticality. We offer two main results. Under the aforesaid conditions, our first main contribution establishes the polynomial decay in time of the survival probability in the spirit of a classical Kolmogorov limit. The second main contribution pertains to the stability, when conditioning on survival, in the spirit of a Yaglom limit. In both cases our proofs work equally well for the analogous setting of non-local superprocesses with non-local branching. Our results complete a series of articles for various families of non spatial branching processes from the 1950s-1970s as well complementing a recent result of this type for spatial branching processes of Ren, Song and Sun (2020) The generality of our results improve on older work of Hering and Hoppe (1981) and Asmussen and Hering (1983) who dealt with a similar context for branching particle systems, as well as providing a general framework for non-local superprocesses.

【9】How weak are weak factors? Uniform inference for signal strength in signal plus noise models
标题 ：弱势因素有多弱？信号加噪音模型中信号强度的统一推断
链接 ：https://arxiv.org/abs/2507.18554

【10】Pathwise analysis of log-optimal portfolios
标题 ：对数最优投资组合的路径分析
链接 ：https://arxiv.org/abs/2507.18232

作者 ： Allan, Anna P. Kwossek, Chong Liu, David J. Prömel
摘要 ：基于cadl ag粗糙路径理论，我们发展了一种路径方法来分析投资组合沿着标准金融市场模型所产生的单个价格轨迹的稳定性和逼近性质。作为投资组合理论的一个典型例子，我们研究了在一个无摩擦的金融市场上经典的投资-消费优化问题中的对数最优投资组合问题.我们确定了一个完全确定性的框架，使路径建设的对数最优投资组合，然后我们建立路径稳定性估计的基础模型参数。我们还得到路径误差估计所产生的时间离散化的对数最优投资组合及其相关的资本过程。
摘要 ：Based on the theory of c\`adl\`ag rough paths, we develop a pathwise approach to analyze stability and approximation properties of portfolios along individual price trajectories generated by standard models of financial markets. As a prototypical example from portfolio theory, we study the log-optimal portfolio in a classical investment-consumption optimization problem on a frictionless financial market modelled by an It\^o diffusion process. We identify a fully deterministic framework that enables a pathwise construction of the log-optimal portfolio, for which we then establish pathwise stability estimates with respect to the underlying model parameters. We also derive pathwise error estimates arising from the time-discretization of the log-optimal portfolio and its associated capital process.

【11】A Jarque-Bera test for skew normal data
标题 ：斜正态数据的Jarque-Bera检验
链接 ：https://arxiv.org/abs/2507.18032

作者 ：Gorgui Gning, Gandasor Bonyiri Onesiphore Da, Oumar Foly Sow, Gane Samb Lo
摘要 ：Azzalin（1985）引入了斜态正态分布律，作为调整与正态分布律共享重要模式的非对称数据的替代方法。它已被广泛研究。然而，为了抓住其正常对应物调查的多样性和丰富性，还有很多工作要做。一般Jarque-Berra检验（GJBT）由Lo et al.（2015），Da et al.（2023）设计，用于至少有有限前八阶矩的任意定律，作为Jarque-Bera（1987）检验的推广，专门为正态数据设置。在这里，我们将其特殊化为扭曲正态数据。当在偏态正态分布中具体化时，该测试被证明在检测任何$\alpha\neq 0$的真实模型方面非常强大，并且无论数据大小都拒绝了正态分布（$\alpha=0$）。为了提高测试效率，我们引入了样本复制方法。
摘要 ：The skew normal law has been introduced in Azzalin (1985) as an alternative to adjusting asymmetric data that share important patterns with the normal law. It has been extensively studied. However, there is so much to do in order to catch the diversity and the richness of the investigation of its normal counterpart. The General Jarque-Berra Test (GJBT) has been devised by Lo et al. (2015), Da et al. (2023) for arbitrary laws with at least finite first eight moments, as a generalization of the Jarque-Bera (1987) test that was specially set up for normal data. Here, we particularize it to skew normal data. When particularized in the skew normal law, this test is proven to be extremely powerful in detecting the true model for any $\alpha\neq 0$ and rejected the normal law ($\alpha=0$) whatever be the size of the data. We introduced the use of the samples duplication method to reach a high level of efficiency for the test.

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